Entry and Asymmetric Lobbying: Why Governments Pick Losers Richard E. Baldwin

Frédéric Robert-Nicoud

Political Science and Political Economy Working Paper Department of Government London School of Economics

No. 3/2007

1

Entry and Asymmetric Lobbying: Why

Governments Pick Losers *

Richard E. Baldwin† Graduate Institute of International Studies, CEPR and NBER

Frédéric Robert-Nicoud‡

London School of Economics, CEP and CEPR

This version: Februray 2007

* We are grateful to Paola Conconi, Gene Grossman, Douglas Irwin, Alan Manning,

Marc Melitz, Doug Nelson, Ricardo Puglisi, Jaume Ventura, Thierry Verdier, two

anonymous referees, and editor Roberto Perotti as well as to seminar participants at

Cergy-Paris, Geneva, LSE, Nottingham, Paris School of Economics, Princeton,

Stockholm, University College Dublin, University of Wisconsin, Zurich, the

conference on Lobbying and Institutional Structure of Policy Making (La Sapienza,

Rome), the CEPR workshop on Trade, Industrialisation and Development (ECARES,

Brussels), the NBER ITI Spring Meeting (Boston), and the Research in International

Economics and Finance conference (CERAS, Paris) for comments and suggestions.

We gratefully acknowledge financial help from the Swiss National Fund (Grant no.

100012-103992/1).

† Graduate Institute of International Studies, Avenue de la Paix 11A, 1202 Geneva,

Switzerland, tel.+41-22-734-8950; fax:733-3049, http://heiwww.unige.ch/~baldwin.

‡ Department of Geography and Environment, LSE, Houghton Street, London WC2A

2AE, UK, tel.+44-20-7955-7604; fax: 7955-7412, http://personal.lse.ac.uk/robertni/.

2

ABSTRACT

Governments frequently intervene to support domestic

industries, but a surprising amount of this support goes to

ailing sectors. We explain this with a lobbying model that

allows for entry and sunk costs. Specifically, policy is

influenced by pressure groups that incur lobbying expenses

to create rents. In expanding industries, entry tends to erode

such rents, but in declining industries, sunk costs rule out

entry as long as the rents are not too high. This asymmetric

appropriability of rents means losers lobby harder. Thus it is

not that government policy picks losers, it is that losers pick

government policy.

JEL H32, P16. Keywords: Lobbying, Sunset Industries,

Sunk Costs.

3

1. Introduction

Governments that try to pick winners and losers usually choose the

latter, according to an old adage. Some of the clearest examples of this

stylized fact come from trade policy. In the United States and Europe,

the most protected sectors (agriculture, textiles, clothing, footwear, steel,

and shipbuilding) have all been in decline for decades. Counterexamples

are rare. Even when a growing sector gets protection, as did the U.S.

semiconductor industry, the protection tends to be focused on market

segments–like memory chips–in which the domestic industry is losing

ground. A related phenomenon is the “NIMBY” syndrome (Not in My

Back Yard), whereby special interest groups seem to fight harder to

avoid losses than they do to achieve gains.

In seeking to account for this phenomenon, the natural place to

start is with the political economy literature. The key approach for our

purposes is the “pressure group” or lobbying approach that was launched

by the classic papers of Stigler (1971) and Peltzman (1976) in the

context of industrial regulation. This approach subsequently found a

natural home in the field of international trade after a series of papers

showed that it provided important insights on why observed trade policy

deviates so radically from welfare-maximizing policies. The path-

breaking papers here are Hillman (1982), which took the political-

support function approach, and Findlay and Wellisz (1982), which

introduced the tariff-formation function approach. More recently, the

pressure-group approach has been extended to include more explicit

4

modeling of how lobbying expenditures affect policymakers’ choices.

Magee et al. (1989) work with a model where political contributions

influence the outcome of elections, but the dominant model in this

literature is now the “protection for sale” model of Grossman and

Helpman (1994). As Rodrik (1995) notes, the great advantage of this

model is that it provides clear-cut micro foundations for lobbying and its

effects in a tractable and fairly general setting.1

1.1. The losers’ paradox

At the heart of the pressure-group approach is the presumption that

special interest groups (SIGs) who spend the most on lobbying or other

political activities are, other things equal, the ones that get the most

government support. Given this view, the success of sunset industries in

winning a disproportionate share of government support is paradoxical.

After all, politicians should value the lobbying dollars of expanding

industries as much as those of declining industries. Moreover, an

industry’s ability to finance lobbying expenditures and its interest in

obtaining government support should be positively related to its size,

employment, and/or profitability; one would expect the highest levels of

government support in the biggest and strongest sectors rather than in

ailing sectors. In the same light, the NIMBY syndrome–observed in

issues ranging from the health-care reform to the location of landfill

1 See Dixit et al. (1997) for a synthesis of the “Protection For Sale” approach and

Baldwin (1987) for a generalization.

5

sites–is curious because lobbying to reverse losses and lobbying to

secure new gains would seem to be equally attractive to special interest

groups.

Our paper uses the pressure-group approach–in particular, that of

Grossman and Helpman (1994)–to account for the surprising amount of

support that goes to declining industries. Our basic story is simple.

Government policy is influenced by pressure groups whose lobbying is

expensive. Special interest groups spend money in order to create rents

that they can appropriate.2 There is, however, a strong asymmetry in the

ability of expanding and contracting industries to appropriate the

benefits of lobbying. In an expanding industry, policy-created rents

attract new entry that erodes the rents. In the extreme, free and

instantaneous entry obviates all rents. This is not true in declining

industries. Since sunk market-entry costs (e.g., unrecoverable

investments in product development, training, and brand name

advertising) create quasi-rents, profits in declining industries can be

raised without attracting entry as long as the level of quasi-rents does not

rise above a normal rate of return on the sunk capital. Plainly, an

asymmetry in the appropriability of rents implies an asymmetric

incentive to lobby. The result is that losers lobby harder, so it is not

government policy that picks losers but rather the losers who pick

government policies. A corollary to this reasoning accounts for the

2 Using U.S. data, Gawande and Bandyopadhyay (2000) provide some evidence that

protection is indeed ‘for sale’. See note 5.

6

observed tendency of special interest groups to fight harder to avoid

losses than they do to win gains.

1.2. Review of the literature

Many explanations of the loser’s paradox have been suggested. One of

the earliest and best-known expositions regards the conservative social

welfare function (CSWF) of Corden (1974). As Corden introduces it,

“any significant absolute reduction in real incomes of any significant

section of the community should be avoided. … In terms of welfare

weights, increases in incomes are given relatively low weights and

decreases very high weights.” Although this sort of government-with-a-

heart description may have a good deal of explanatory power, it comes

close to assuming the answer. Moreover, at least in developed nations,

governments have a great many policies for redistributing income and

cushioning shocks (income taxes, unemployment insurance, retraining

schemes, etc.) and so, even if “caring” were a major motive in

government policy, an optimizing government would separate industry

support from pure income distribution considerations. An even more

important critique is that the conservative social welfare function does

not explain why some declining industries do not win massive

government support. In the 1980s, for instance, the real wages of U.S.

unskilled workers fell substantially but only a small subset of these

attracted government support. As the work of Goldberg and Maggi

(1999) shows, it was the well-organized sectors (e.g., U.S. apparel

workers) that induced the US government to adopt distortionary policies

7

that softened the fall in their real incomes. In the same spirit as the

CSWF approach are the equity-concern model of Baldwin (1982) and

the status-quo model of Lavergne (1983).

One of the most intuitive explanations for the loser’s paradox

turns on Anne Krueger’s use of the “identity bias” to account for what

she calls “asymmetries in the political market.” The bias, according to

Krueger (1990), reflects the fact that people care more about the welfare

of known specific individuals than that of unidentified faceless

individuals. To see how such a bias could explain asymmetric

government support, the author contrasts the impact of a subsidy to a

declining sector with one to an expanding industry. Both subsidies will

alter the allocation of employment, but in the ailing industry the jobs

“saved” are identified ex ante with specific individuals whereas the jobs

created in the expanding sector cannot be identified with any specific

individual, ex ante. In a way, this model provides psycho-micro

foundations, of the type associated with Schelling (1984), for the CSWF

approach. As such, Krueger’s explanation relies on the shape of the

policymakers’ objective function and thus shares the shortcomings of the

CSWF solution. Likewise, Rotemberg (2003) proposes a theory in which

a small degree of voter altruism in direct and representative democracies

alike yields protection to import-competing sectors in which the level of

income of the sector-specific factor is low.

A related paper that relies on more standard microeconomic

behavior is Fernandez and Rodrik (1991). These authors use a

mechanism that is related to the notion of identity bias in order to

8

account for the reluctance of governments to adopt changes in policies

(i.e., reforms). To see this, consider a simple economy with 45% of

workers in one sector, 55% in another, and a hypothetical reform that

will help workers in the initially small sector and hurt those in the

initially big sector. Moreover, the reform will shift employment so that

60% of workers are eventually in the sector that is helped—that is, the

sector that was initially small. If each worker knew what her fate would

be ex ante, then the reform would easily garner support from a majority

of workers. However, workers in the initially larger sector do not know

ex ante in which sector they will end up ex post; the probability that they

move to the helped sector is quite small, just 15/55, so each one of them

may oppose the reform ex ante. Observe that, although the identity bias

operates via the psychology of policymakers in the Krueger model, the

Fernandez–Rodrik model relies on nothing more than individual

rationality and the assumption of a random selection device.

Another solution to this puzzle that displays solid

microfoundations is proposed by Hillman (1989), who views the use of

trade policy as a "social insurance" against exogenous changes in

comparative advantage; this model could account for the asymmetric

protection of losers. Although it is difficult to discern the underlying

forces in their model, Magee et al. (1989) also claim to explain

asymmetric protection with their "compensation effect."

Sauré (2005) argues that subsidies to importing industries

represent a crucial piece in trade agreements. If free trade leads to

complete specialization then each country has an incentive to set tariffs

9

that improve its own terms of trade, making the free-trade agreement not

enforceable. Subsidies reduce the incentive to engage in a trade war: by

subsidizing their own comparative-disadvantaged industries, countries

limit one another’s abilities to manipulate world prices in their favor. In

contrast, we emphasize the role of lobbying and the role of asymmetric

shocks at the sectoral level (e.g., a surge in imports rather than the level

of imports per se) in explaining asymmetric protection.

Another line of research that is tangentially related to the losers’

paradox is the study of the collapse of senescent industry. The seminal

papers, Hillman (1982) and Cassing and Hillman (1986), apply the

political-support function approach to understand why declining

industries continue to decline despite the protection they receive, putting

a special emphasis on their eventual collapse. Subsequent important

contributions include Matsuyama (1987), Van Long and Vousden

(1991), and Brainard and Verdier (1997). Although this branch of the

literature is also concerned with sunset sectors, its focus is quite different

in that it takes as a starting point the fact that declining industries will

receive protection; our paper seeks to understand why this is so.3

3 Many of these papers also continue to conjecture why declining rather than expanding

industries so frequently garner government support, but this is not their main focus. In

particular, Brainard and Verdier (1997) suppose that credit constraints prevent an

expanding sector from investing in the lobbying it needs to get protection. Also,

Hillman (1989) discusses the asymmetrical effects of entry, but they are not

incorporated into his formal model.

10

The main idea in our model is based on an unpublished

manuscript by one of the authors, Baldwin (1993), but our paper differs

significantly in its modeling strategy and in the rigor of its analysis.

Baldwin (1993) relied on unanticipated but permanent changes in the

degree of foreign competition to generate differences between winners

and losers, not explicitly allowing for the simultaneous existences of

both types.4 This paper generalizes Baldwin (1993) by using a model in

which different industries face idiosyncratic temporary demand shocks,

agents are forward looking, and policy setting is intertemporal. We also

note that Grossman and Helpman (1996) extended the basic asymmetric

lobbying framework of Baldwin (1993) by considering the free riding of

new entrants in “winning” sectors. Their main argument is that it is free

riding rather than entry that causes the asymmetry; we shall revisit this

issue.

It is worth stressing that our proposed solution based on sunk-

cost is complementary to all the aforementioned solutions.

1.3. Empirical studies of the losers’ paradox

The lobbying success of losers–the losers’ paradox–has been extensively

documented empirically. In the United States, Hufbauer and Rosen

4 The novel mechanism we are proposing in this paper combines negative shocks and

the importance of sunk entry costs within a given industry. Marceau and Smart (2003)

propose a theory in which sectors that rely heavily on sunk costs are more successful in

obtaining tax breaks.

11

(1986), Hufbauer et al. (1986), and Ray (1991) have documented that

declining industries receive a disproportionate share of protection.

Particularly favored industries are agriculture, textiles, footwear,

clothing, and steel, all of which have experienced secular declines in

employment and GDP shares in the United States. In their introduction,

Hufbauer and Rosen (1986) write:

With bipartisan regularity, American presidents since Franklin

D. Roosevelt have proclaimed the virtues of free trade. They

have inaugurated bold international programs to reduce tariff

and non-tariff barriers. But almost in the same breath, most

presidents have advocated or accepted special measure to

protect problem industries. ... The United States is not the only

country to have experienced competition in mature industry

from foreign goods. Most industrial countries, in Europe, Japan

and elsewhere, have encountered similar difficulties.

More directly related to our issue, many econometric studies

have found that being a “loser” in terms of employment, output, or

import competition actually helps an industry get more protection.

Baldwin (1985) and Baldwin and Steagall (1994) find a strong

correlation between positive "serious injury" findings of the U.S.

International Trade Commission and reduced industry profits and

employment. Glismann and Weiss (1980) find that above-trend income

increases are correlated with reduced protection in Germany between

1880 and 1978. Marvel and Ray (1983) find that an industry’s growth

rate has a negative impact on its level of protection. This is confirmed by

12

Baldwin’s (1985) finding that the industries most successful at resisting

tariff cuts in the Tokyo Round were characterized by, inter alia,

relatively slow or negative employment growth as well as by high and

rising import penetration ratios. More recently, econometric evidence

from Ray (1991) shows that declining industries tend to get more

protection and Trefler (1993) finds that an increase in import penetration

tends to increase the level of protection a sector is afforded.5

Furthermore, a number of econometric studies have found that average

tariff levels tend to rise in recessions (see e.g. Ray 1987; Hansen 1990;

O’Halloran 1994). Gallarotti (1985) finds similar results concerning U.S.

tariffs in the 19th and 20th centuries. In a similar light, the time-series

approach of Bohara and Kaempfer (1991) shows that tariffs are Granger-

caused (positively) by unemployment and real GNP. In ongoing work on

U.S. data, Baldwin et al. (2006) regress lobbying expenditure on the

interaction between negative demand shocks and measures of “sunk-

ness” of capital (in addition to a group of controls) and some

specifications report a positive coefficient in line with theory.

Interestingly, the coefficient of demand shocks alone is not significant in

a statistical sense; it is only when interacted with a measure of sunk-ness

that demand shocks become significant.

5 Interestingly, Gawande and Bandyopadhyay (2000), who explicitly test the

Grossman-Helpman framework using cross-industry data on the coverage ratio of U.S.

non-tariff barriers coverage ratios and US lobbying spending, find a negative

relationship between import penetration and the level of protection when the sector is

not organised; this relationship is positive otherwise.

13

We also note that the systematic favoring of losers is actually

inscribed in international and national trade laws. The General

Agreement on Tariffs and Trade (GATT) generally prohibits countries

from pursuing policies that favor domestic firms over foreign firms. The

major exceptions to this principle (safeguards, dumping duties, and

countervailing duties) involve situations where imports cause or threaten

to cause material injury to an established industry. In contrast, there are

no general exceptions that allow a country to promote the interests of an

expanding industry. These principles can also be found in national laws.

For example, U.S. trade laws make “decline” (appropriately interpreted)

an explicit requirement for trade protection.

If one accepts the view that political economy forces shape

national and international trade laws, then the foregoing asymmetry is

puzzling. Lobbying dollars of expanding industries should be just as

welcomed by politicians as the dollars of declining industries. It is

therefore odd that politicians should have adopted laws that greatly

restrict their ability to promote profits in expanding sectors even as they

create loopholes that boost the profits of declining industries.

1.4. Plan of the paper

The paper is structured as follows. Section 2 develops the static

economic and political-economic model. Section 3 introduces the

dynamic structure of the model and solves the game allowing for entry.

Section 4 considers two extensions, and Section 5 summarizes the

14

results of the paper and discusses some of the policy implications of our

analysis.

2. The basic model

Formalization of the asymmetric lobbying effects discussed in the

Introduction requires a model that first shows how industry support

affects the fortunes of firms that may lobby and then connects these

changing fortunes to the political decision-making process. Toward this

end we present a simple model whose special features simplify the

algebra; we shall argue, however, that the basic results in the paper do

not qualitatively depend upon these special features. In particular, we

combine a standard monopolistic competition model (which can be

thought of as the closed economy version of a “new” trade model à la

Flam and Helpman 1987) with the lobbying model of Grossman and

Helpman (1994).6

6 Typically, the new political economy literature works with a Ricardo–Viner model. In

our model, since capital investments are sunk, it follows that capital is sector specific,

like in the Ricardo–Viner framework. In contrast to that framework, however, neither

the returns to the factor that is mobile across sectors (labor) nor the returns to the

factors specific to other sectors are affected by the shocks or by the protection granted

to a sector in particular. This is a consequence of the quasi-general equilibrium nature

of our model which features quasi-linear preferences and a constant-return-to-scale

numéraire sector that uses labor only.

15

2.1. Tastes and technology

Consider an economy with 1M + sectors. The “plus one” sector uses

labor L to produce a homogenous good A under constant returns and

perfect competition. By choice of units, one unit of L produces one unit

of A. There is also a large number M of symmetric industrial sectors that

are characterized by increasing returns and monopolistic competition. A

typical firm faces variable costs equal to βwx, where x is the firm output,

β is the unit labor requirement, and w is the wage. In this section, to fix

ideas we take the number of firms as given, delaying considerations of

entry to Section 3. When entry is allowed, we assume that a new

manufacturing firm needs to sink one unit of capital in order to operate,

with this capital produced by using L only.

Instantaneous utility is linear in the consumption of A and a two-

tier index of industrial goods consumption:

(1) / 1 1/ 1/(1 1/ )

1 0ln , ( d ) ,

mNM

m m m m mjm jU A D D N c jχ σ σ σα − − −

= == + ≡∑ ∫

and σ>1. Here Dm is the CES (constant elasticity of substitution)

consumption index for a typical industrial sector m, cmj is the

consumption of variety j in sector m, Nm is the number (mass) of such

symmetric varieties within a typical sector, σ is the constant elasticity of

substitution among varieties, and αm is a demand shift parameter. The

number of differentiated product sectors M is fixed.

Note that the inclusion of the parameter χ makes the CES

aggregate Dm more general than the usual functional form. The

parameter χ measures the preference for diversity. In the standard love-

16

for-variety preferences, χ is taken to be zero, implying that consumers

could become unboundedly happy by consuming an infinitely small

amount of infinitely many varieties. To avoid this feature and to simplify

our algebraic expressions, we neutralize the love-of-variety aspect by

taking χ=1.

Importantly, we assume random preferences in the following

sense: αm is either αH or αL, where αH>αL; that is, each sector faces

either high or low demand.7

The model features a continuum of consumers endowed with a

share–equal to s(i) for consumer i–of the economy’s labor and of all

firms’ equities, so that the individual budget constraint is

(2) 0

1 1

( )( ) d ,m

M M N

m A i m mj mjjm m

s i wL T p A p c jτ=

= =+ Π − = +∑ ∑∫

where Πm is the total operating profit from all sector-m firms, L is the

economy wide labor endowment, T is the total lump-sum tax collected,

and τ is an ad valorem tax or subsidy factor (i.e., the rate is τ –1, which

is a tax if positive or a subsidy if negative). Producer prices are denoted

as p, so consumer prices are τp (τ is fully passed on to consumers under

Dixit–Stiglitz monopolistic competition).

We normalize the economy’s total labor endowment to unity.8

Hence the optimal aggregate demand for a typical variety j in a typical

sector m and the aggregate demand for A and are respectively given by

7 Our qualitative results would hold if we assumed technology shocks rather than

demand shock (more on this in Section 4.2).

17

(3) 0

1 1

1

0

d( )

, .( ) d

m

m

M M N

m m mj mjjm m mj m mmj N

Am mjj

w T p c jp

c App j

σ

σ

τα τ

τ

−=

= =

−

=

+ Π − −= =

∑ ∑∫

∫

As usual, the producer price pmj of a typical industrial firm j is related to

marginal costs according to the expression pmj(1-1/σ) = βw. By choice of

units (viz. β = 1-1/σ) and taking L as numéraire, we can without loss of

generality set pmj = 1 for all firms in all M sectors. Consequently, a

typical firm’s flow of operating profit is given by9

(4) , , ,mm m L H

m mN

απ α α αστ

= ∈

and Πm ≡ Nm πm is total operating profit in sector m (within-sector

symmetry allows us to drop the firm subscript). Using the ex ante

symmetry of sectors, it proves convenient to index sectors by the state of

demand faced, denoting the Π earned by those facing high and low

demand as ΠH and ΠL, respectively; clearly ΠH > ΠL for any given level

of τm.

2.2. Utilitarian benchmark

In the sequel we shall introduce a political process governing the choice

of τ, but intuition is served by first identifying the socially optimal τ.

8 Accordingly, we assume that Σmαm is small enough that production of A is always

positive at equilibrium.

9 The result follows by rearranging the firm’s first order condition to (pmi – βw)cmi =

pmicmi/σ and then using the demand function and symmetry of varieties.

18

Specifically, the government chooses sector-specific taxes (τ>1) or

subsidies (τ<1) to maximize aggregate welfare as measured by a scalar

a/(1+a) times the sum of consumers’ utility.10 The A-sector is untaxed

and the lump-sum tax T is adjusted to maintain a balanced budget. By

symmetry of firms, the lump-sum tax revenue (which may be negative)

required to implement the vector τ is just the sum over all m of (1–

τm)Nmcm. Using (4) together with the solutions for T, p, and cm in (1), we

find that the Benthamite objective is

(5) 1

1 1/1 ln( ) , 0,

1

Mm

mm m m

aW a

a

α σατ τ=

− ≡ + − > + ∑

where we have normalized pA to unity by choice of units of A.11

Maximizing this with respect to τm for all m requires that the

government offsets the only distortion in the economy—namely, the

monopolistic pricing distortion—and this implies that the optimal

utilitarian policy is

(6) 1

1mτ βσ

= ≡ −

for all M sectors. This result clearly entails a subsidy (τ <1 is a subsidy

whereas τ >1 is a tax) to all industrial sectors because σ >1. Note also

that, since there is only one distortion and since lump-sum taxation is

possible, the Benthamite government can attain the first-best outcome.

10 We introduce a (without loss of generality) in order to facilitate comparison with (8),

where a is necessary.

11 See the Appendix A.1. for details of the calculation.

19

With this utilitarian benchmark in hand, we turn to the lobbying game,

where the policymaker may be influenced by political contributions.

2.3. Lobbying

Hillman (1989) and Baldwin (1985) point out that, under realistic

assumptions, elected officials may not be fully aware of the economic

interests of their constituents, and their constituents may not be familiar

with all the policies (and their economic consequences) championed by

their elected representatives. Consequently, as Baldwin (1985) notes, a

group of voters "may have to engage in time-consuming and costly

lobbying activities to bring its viewpoint to the attention of legislators.

Similarly office-seekers need funds to inform the voters of how they

have served them or will do so in the future." The so-called pressure–

group model (or lobbying model) developed by Olson (1965) and others

focuses on the costs and benefits of lobbying and its impact on policy.

This class of models abstracts from electoral politics, assuming that the

government is entrenched or at least that every elected government will

react in the same way to lobbying.

Explicit consideration of such imperfections would require a

model that is much more complicated than the one needed to examine

the basic logic of asymmetric lobbying. Thus, following standard

practice (see e.g. the political support function approach of Hillman

1989 and the formal lobbying approach of Findlay and Wellisz 1982),

we skip the micro modeling of how lobbying funds influence policy

choices. Instead, we follow the approach in Grossman and Helpman's

20

seminal 1994 paper in which lobbying expenditures in the form of

“contributions” are just assumed to directly enter the objective function

of the government.

Specifically, we follow Grossman and Helpman (1994) as

simplified in Baldwin and Robert-Nicoud (2006); that is, we model

lobbying as a menu auction (Bernheim and Whinston 1986) and we

assume that all industrial sectors are perfectly organized in the

Grossman–Helpman sense (i.e., all firms in a sector act as one when it

comes to political contributions). Contributions made by sector m are

denoted as Cm. Consumers and the untaxed A-sector are unorganized and

thus do not lobby.

Government’s objective, lobbies, and contributions

As in Grossman and Helpman (1994), the government’s objective

function Ω is a weighted sum of lobby contributions and aggregate

social welfare W:

(7) 1

1; 0,1, 0,1 ,

1

M

m m m m mm

W G I C G I ma =

Ω = + ∈ ∈ ∀+ ∑

where the first term /(1 )W aU a= + is the utilitarian social welfare

function from (5) and where the second term represents total political

contributions. The binary variable Gm reflects the fact that the

government always has the option of rejecting contributions from any

sector, and the binary variable Im reflects the lobbying choice of a

21

particular sector (Im = 0 implies no lobbying).12 By way of interpretation,

note that a pure Benthamite government would be characterized by a=∞

and a pure “Leviathan” by a = 0, so a captures the extent to which

governments care about social welfare as opposed to political

contributions. Mitra (1999) adds a lobby formation stage to the

Grossman–Helpman setting. He assumes an exogenous fixed cost of

getting organized, which differs across sectors, and studies how this

affects the equilibrium outcome. By contrast, we assume that the fixed

cost of lobbying is zero for all m, and we endogenize the decision to

lobby actively or not. This decision is taken according to an external

factor that has nothing to do with an exogenous cost of lobbying per se.

The vectors τ and G are the government’s choice variables.

Lobbies contribute in order to induce the government to deviate from the

utilitarian first-best outcome. As in the Grossman–Helpman model, we

restrict contributions to be globally “truthful”. Thus, if an industrial

sector m decides to lobby (i.e. Im = 1) then its contribution is Cm(τ) =

Πm(τ)–Bm, where Bm is a scalar; if it decides not to contribute (i.e. Im = 0)

then Cm(τ) = 0 for all τ.13 Here B is the vector of which Bm is a typical

element.

12 In our model, at equilibrium the government will always accept contributions. In a

setting where lobbies’ interests are correlated and where the elected candidate bargains

with the lobbies, Felli and Merlo (2006) show that the elected candidate sets Gm = 0 for

some m at equilibrium.

13 Locally truthful strategies are the only ones to survive the “coalition proofness”

refinement introduced in Bernheim et al. (1987).

22

The all-lobby outcome

An equilibrium in this world is defined by the government’s strategy

(i.e., the vectors τ and G) and the M-sectors’ strategies (i.e. the vectors I

and B) that are mutual best responses. The payoff function of a typical

sector m is Πm–Bm. The government’s payoff function can be written as

(8) 1 1

11 ln( ) ( ),

1 1

M Mm m

m m m mm mm m m

aI G B

a a

α αβατ τ τ σ= =

Ω ≡ + − + − + + ∑ ∑

where we have used equations (4) and (5) and the fact that contributions

are truthful.

We shall calculate the B–values later. Taking them as given for

the moment, we investigate what policy would be chosen if a typical

sector chooses to make contributions and the government chooses to

accept them (i.e., if Im = Gm = 1 for all m). In this politically influenced

case, the typical element of τ that maximizes (8) can be shown to be

(9) .mm

I

aτ β

σ= −

Three remarks are in order. First, recalling that β≡1-1/σ is the

first-best subsidy, the subsidy in the lobbying equilibrium equals the

utilitarian benchmark only when the government is benevolent (a = ∞)

or when no group contributes (Im = 0 for all m). Second, (9) shows that

the acceptance of contributions induces the government to subsidize a

sector beyond the social welfare maximizing level. This allows the

sector to sell more as it continues to price monopolistically. Third, as a

result of the government payoff functional form, each sector’s τm

23

depends only on the sector-specific organization variables and

parameters, with the subsidy decreasing in the profit margin 1/σ and

decreasing in the parameter a that measures the government’s concern

for social welfare.14

Characterization of the equilibrium is facilitated because the

government’s participation constraint is binding only in equilibrium (as

usual in the Grossman–Helpman approach). Thus, the B–values are

chosen by lobbies to make the government just indifferent between

allowing τ to be influenced by accepting contributions and choosing its

outside option, which is to refuse contributions from a sector and set that

sector’s subsidy to the utilitarian optimum described in (6). That is,

assuming all other sectors are lobbying and contributing, sector m’s

contribution (which equals Πm–Bm) must be large enough to make the

government indifferent between accepting its contribution (i.e., choosing

Gm = 1 (and thus setting τm = β –1/aσ) and refusing its contribution (i.e.,

choosing Gm = 0 and thus setting τm = β). In symbols, the equilibrium Bm

must satisfy

(10) * (ln ) (ln 1)

1 1/ 1/

1[ ] 0,

1

dev m mm

m m

a

a a a

Ba

α αβαβ σ β σ β

Ω −Ω ≡ − − − + − −

+ Π − =+

where Πm is evaluated at τm = β –1/aσ. Here Ω* is the government’s

payoff in the all-lobby outcome–namely, (8) evaluated at τi = β –1/aσ

14 This is because of the additively separable preferences; generally, all parameters

would be relevant.

24

for all i with all sectors contributing–and Ωdev is the government’s payoff

when all sectors except sector m contribute (i.e., when τi =β –1/aσ and

Gi = 1 for all i but m, and Gm = 0, and τm = β).

The Nash equilibrium

In order to show that the all-lobby outcome is a Nash equilibrium with

(9) giving the equilibrium τ –values, we show that a typical sector gains

from lobbying when its contribution is large enough to induce the

government to accept it. The informal argument is quite simple. A

sector’s contribution induces the government to choose a policy that–

although suboptimal from the utilitarian perspective–transfers money

from consumers to firms. To respect the participation constraint, a

sector’s net contribution need only compensate the government for the

reduction in social welfare (i.e., the reduction in the W part of Ω).

Because the social welfare loss is of second order while the transfer is of

first order, all sectors will indeed find it in their interests to contribute.

Finally, the government is (by construction) just indifferent to deviating

from the equilibrium, so its strategy of accepting contributions is Nash.

Observe that since the inequality is independent of the state of demand,

it follows that both high and low demand sectors would lobby. We

summarize this intermediate result as follows.

Result 1: When entry is impossible, the outcome where all sectors lobby

regardless of the state of demand is part of a Nash equilibrium. In this

all-lobby outcome, the levels of subsidies are given by (9). Moreover, the

25

outcome where lobbying is done only by sectors facing low demand is

not a Nash equilibrium.

Proof. The proof of this result boils down to the proof of a simple

proposition. By construction, the equilibrium B–values are set to induce

the government to accept all contributions, and so all we need to show is

that a typical sector will want to lobby. To this end, two facts are useful:

(i) τm equals β–1/aσ if sector m lobbies and equals β otherwise; and (ii)

operating profit is decreasing in τm (i.e. increasing in the subsidy rate 1–

τm). Given these facts, a sector can gain from lobbying provided that the

contribution it must pay to the government is sufficiently low.

Specifically, denoting the sector-m operating profit function as Πm[⋅], the

net profit from lobbying must exceed the net profit from not lobbying:

Πm[β–1/aσ] – Cm > Πm[β]. Given that contributions are truthful, our task

is then to show that Bm > Πm[β].

The Nash equilibrium Bm is determined by (10), which–using (4)

and (9)–can be written as

(11) / 1

ln( ) ln( ) 1 , * .* * *m m m

m mB aa

α α α σβα τ βτ τ β τ σ

= − − − + ≡ −

Equation (4) implies that Πm[β] = αm/σβ, so lobbying is worthwhile to

sectors if the following inequality holds:

(12) 1 1 1 1 1 1 1

(ln ln ) ( ) ( )1 * * *

0.

m

a

a aα β

τ β τ β σ τ β

∆ ≡ − − − + − +

>

Observe that either the inequality holds for sectors facing both low and

high states of demand, or else it does not hold for any sector.

26

Because of the log functions’ concavity, ln(1/τ*) – ln(1/β)

exceeds τ*(1/τ* – 1/β). Substituting this into (12) and rearranging terms,

we see that ∆ is greater than something that equals zero:

1 1 1( * )( ) 0.

1 *m

a

a aα τ β

σ τ β∆ > − + − =

+

The right-hand side equals zero by definition of τ*; see (11).

Finally, this reasoning shows that any equilibrium in which some

sectors are not lobbying fails to be a Nash equilibrium because each

sector would unilaterally gain from lobbying. QED.

3. Entry and the incentive to lobby

We now extend the model to continuous time and allow the number of

firms in a typical sector to be determined via free entry.

3.1. Additional assumptions

The representative agent maximizes her lifetime utility, which is

assumed to be additively separable and equal to0

drt

te U t

∞ −

=∫ , where U is

as in (1) and r > 0 is the discount rate. The representative agent can

choose either to consume her income or to invest it in shares of new

firms. Preferences are random; the switching between αL and αH is

governed by a symmetric Markov process (see Table 1).

Creation of a new industrial firm in any of the M sectors entails a

fixed cost consisting of one unit of capital (this cost reflects market entry

costs as in Baldwin’s (1988) model). One unit of capital is produced

27

from F units of labor under conditions of perfect competition, so the

entry cost equals F. Importantly, this capital is sunk in the following

sense: once a unit of capital is built, it must be either employed in the

sector in which it was invested or abandoned (since all consumers are

identical, no firms will be sold in equilibrium). In addition, capital does

not depreciate.15

Our next task is to characterize the entry decision.

Table 1: The Markov transition matrix

3.2. Entry

Entry, as usual, is assumed to occur instantaneously and up to the point

where the equilibrium value of firms is no greater than the entry cost F.

Owing to the stochastic demand, a single firm will have different values

depending on the current state of demand (high versus low).

15 Adding depreciation is uncomplicated (see Section 4.3) but is not necessary here.

Transition probabilities

αL αH

αL 1–λdt λdt

αH λdt 1–λdt

28

Value of the firms at steady-state

The value V of a typical firm in a typical sectoris the discounted value of

operating profits net of any lobbying contribution.16 By symmetry, there

are only two levels of V: one for firms belonging to low-demand sectors,

VL, and one for firms belonging to high-demand sectors, VH.

Specifically,

(13) [ ][ ]

d d (1 d ) , ( ) / ,

d d (1 d ) , ( ) / ,

rdtL L H L L L L L

rdtH H L H H H H H

V b t e tV t V b I C N

V b t e tV t V b I C N

λ λ

λ λ

−

−

= + + − = Π −

= + + − = Π −

where we omit the time and sector subscripts since these values are

constant at steady state and since sectors face either high or low demand.

Note that the values for b (a mnemonic for benefit) are the per-firm

operating profit net of any contributions, so bi = Bi/N, for i = H, L.

These equations are easy to interpret. For VL, the value of a firm

in state L at time t is equal to the current flow of net profits plus the

expected discounted value it will have at time t+dt: with probability λdt

it will move to state H and with probability 1-λdt it will remain in state

L. The value VH is defined analogously. In the limit of continuous time

as dt→0, by symmetry among industries and firms within industries we

have, after rearranging:

16 As a special feature of our functional forms, total operating profit per sector is

independent of the number of firms per sector; the key point is that V is diminishing in

N.

29

(14)

( ), ( )

( ) ( ), .

( 2 ) ( 2 )

L L H L H H H L

L H H LL H

rV b V V rV b V V

r b b r b bV V

r r r r

λ λ

λ λ λ λλ λ

= + − = − −⇔

+ + + += =+ +

The first two expressions are standard asset-pricing equations: r times

the expected value of the firm must equal the sum of the current flow of

net profits and the expected capital gain. The latter two expressions are

the solutions for each V in terms of b.

Because the cost of entry is F, free-entry requires that the steady

state number of firms per sector rises until the maximum value of a

typical firm equals F. A firm’s value may differ between high– and low–

demand states; hence the entry condition is

(15) subject to max , .H LN V V F=

Note that U in (1) is quasi-linear, so the transition dynamics are

degenerated. That is, Nm jumps to its steady-state value N* as soon as αm

= αH. (It jumps to some N0 < N if αm = αL initially, as we shall explain).

3.3. The only-losers-lobby equilibrium

We assert that the outcome in which only sectors facing low demand

lobby is a Markov perfect equilibrium (MPE), and we refer to it as the

“only losers lobby” (OLL) outcome. In this dynamic version of the

model, the state variables are (i) N, the number (mass) of firms in a

typical sector–a number that is influenced by players’ actions via free

entry–and (ii) α, the vector of the states of demand facing each sector.

Given our simple setup, a sector’s strategy can be summarized by its

30

decision on whether or not to lobby, with this action possibility

depending upon the state of demand. Formally, the OLL equilibrium can

be expressed as the set of sector strategies such that

(16) 0 if ,

1 if .m H

mm L

Iα αα α

== =

Here Im = 1 or Im = 0 indicates that sector m is or (respectively) is not

lobbying. Note that since there is irreversible entry and since Dixit–

Stiglitz monopolistic competition never produces negative operating

profit (Dixit and Stiglitz 1977), the number of firms that are active in

each sector is constant in steady state. This and symmetry of firms

allows us to drop the sector subscript from the N–terms. In this outcome,

the values of a typical firm are

(17)

( ) ( ), ;

( 2 ) ( 2 )

1( ), .

( 1/ )

OLL OLLL H H LL H

L HL H

b r b b r bV V

r r r r

b B bN a N

λ λ λ λλ λ

α ασ β σ σβ

+ + + += =+ +

= − =−

The superscript “OLL” is used to denote the value of firms in sectors

implementing the only–losers–lobby strategies.

To demonstrate that the OLL outcome is an MPE, it is useful

first to establish that, for any given N, the value of a firm when it faces

low demand is no greater than its value when it faces high demand; that

31

is, OLL OLLL HV V F≤ = . This feature is intuitively obvious and easy to

establish formally.17

Figure 1 helps us interpret the equilibrium by plotting values of a

typical firm against the number of firms per sector. Since competition

lowers per-firm value, all lines slope downward. The second and third

lines (counting from the top) indicate the only-losers-lobby outcome for

sectors facing high and low demand. These are marked OLLHV and OLL

LV ,

respectively; the OLLHV line is above the OLL

LV line. Free entry means that

the value of a firm can never rise above F, so all the value lines are cut

off at the horizontal line at F. Plainly, the steady-state number of firms is

N* in the OLL outcome. The value of firms facing high demand will be

F; point 2 gives the value of firms facing low demand.

17 The proof is by contradiction. If VOLLL > VOLL

H then the free entry condition implies

F = VOLLL, so F > VOLL

H. This in turn implies that the high-demand sector could lobby

without attracting entry and so, by Result 1, it would. Since this contradicts the

definition of the only-losers-lobby outcome, we know that VOLLL ≤ VOLL

H = F. This in

turn implies bL ≤ bH.

32

Figure 1: The free-entry equilibrium

Establishing the Markov perfect equilibrium

Using the diagram, we can show that the only-losers-lobby outcome is a

Markov perfect equilibrium. We start with the government. At every

time t, the government cannot, by construction of B, gain from deviating

from the OLL outcome. Thus, accepting contributions and providing the

politically influenced τ is part of a Nash equilibrium in every subgame

and in every state of the world. The argument for high-demand sectors is

similar. No high-demand sector could gain from deviating; after all, free

entry ensures that the value of a typical firm cannot rise above F, so any

lobbying effort would be useless. Thus, the strategy of no lobbying in

high-demand states is Nash in every subgame.

F

N

VHAL

VHOLL

VLOLL

VLOLL,dev

N**N*

1

2

3

4

5

6

€

VLAL

=

N0

0

33

Finally, low-demand sectors cannot gain from deviating because

ceasing to lobby would lower their value from point 2 to point 3 in the

diagram. More specifically, under this deviation the value of a typical

firm facing low-demand sector would be [λbH+(r+λ)bLdev]/[ r(r+2λ)],

where bLdev is the per-firm operating profit in the low-demand state when

the subsidy is the socially optimal β (i.e., when bLdev = αL/(σβN)). The

proof of Result 1 showed that one-period lobbying is always worthwhile

when it does not change N, so we know that

/[ ( 1/ )]/L Lb B a Nα σ β σ= − + − exceeds bLdev. Using (14) this tells us

that not lobbying in the low-demand state would lower the typical firm’s

value.

We summarize these findings in our next result.

Result 2: Because free entry makes lobbying useless for sectors facing

their entry margin (i.e., for high-demand sectors), the only-losers-lobby

outcome is a Markov perfect equilibrium. However, firms in sectors

facing low demand find their values below entry costs, so lobbying can

raise their value.

As it turns out, the OLL outcome is not the only MPE, as

Grossman and Helpman (1996) have pointed out.

3.4. Other equilibria

Starting from N = N*, lobbying in the high state does no good–but

neither does it harm firms facing high demand. If (for whatever reason)

incumbents in a sector with high demand actually did lobby, this would

34

induce more entry and thus an increase in the equilibrium number of

firms to N** in the diagram. It is important to note that , once the new

entrants are irreversibly in the market, a deviation by cessation of

lobbying in the high-demand state would lower the value of the firm

from point 4 to 5 in the diagram, so no deviation would occur in the

high-demand state. Likewise, no deviation would occur in the low-

demand state, so this outcome–what we call the “all lobby” outcome,

denoted as “AL” in the diagram–is also an MPE. We summarize this as

follows:

Result 3: Given free entry, the all-lobby outcome is a Markov perfect

equilibrium because, once high-demand lobbying has increased the

number of active firms, cessation of lobbying would lower the value of

such firms. As before, sectors facing low demand can raise their value

by lobbying, so lobbying in both states is also a MPE.

It is possible to arrive at the N = N** state because lobbying in

the high-demand state starting from N = N* is both useless and costless

in terms of incumbent firms’ value in the high-demand state.

Dominance of only-losers-lobby MPE

Although this second MPE does exist, there are good reasons for

believing that it would never occur. The basic argument is that, even

though the increase in the number of firms from N* to N** does not

affect VH, it will lower the value of firms facing low-demand returns.

Note that the value of a typical firm facing high demand is identical

(namely F) in the two MPEs, but the value of a typical firm facing low-

35

demand is lower in the all-lobby outcome. To see this, observe that from

(14) with VH = F, we have VLi equals (bL

i+λF)/(r+λ), where i denotes

either “OLL” (in the only-losers-lobby equilibrium) or “AL” (in the all-

lobby equilibrium). Since bL is given by (16) with αm = αL and since

N** > N*, it is clear that ALLV is lower than OLL

LV (these values

correspond to points 2 and 6 in the diagram). In short, although the

lobbying-induced entry has no effect on the value of firms facing high

demand, the presence of more firms lowers the value of the same firms

in the low-demand state. Our next result summarizes this reasoning.

Result 4: The only-losers-lobby and all-lobby outcomes are both MPEs,

but the former dominates the latter in the sense that firms are indifferent

between the two when facing high demand yet strictly prefer the OLL

equilibrium when facing low demand. This makes the only-losers-lobby

MPE focal.

4. Extensions

In this section we consider three extensions of our analysis. We first

allow for the possibility that new entrants “free ride” on the lobbying

contributions by former incumbents for some time. We then show that

assuming technological shocks yields the same qualitative results as in

the case of demand shocks described thus far. Finally, we apply our

model to sunset industries–namely, for the case of permanent adverse

shocks.

36

4.1. Free riding

In the spirit of the Grossman–Helpman lobbying approach, our basic

model assumes that all firms in a sector are politically perfectly

organized in the sense that they act as one when it comes to presenting

and financing a contribution menu to the government. To deal with

entry, we extend our basic model in the simplest possible way: by

supposing that all entrants immediately act as incumbents. This of

course is not the only reasonable assumption (see Grossman and

Helpman 1996 for discussion of the issue) and, as we shall see, relaxing

this assumption has important implications for Result 3.However, we

shall demonstrate that this assumption does not alter (and even

reinforces) our main result that free entry removes the incentive for

lobbying in sectors facing their entry margin, since when profits are

above the standard value they are immediately and successfully grabbed

by entrants.

Modeling free riding

To model free riding by entrants, we assume that new firms do not share

the financing of contributions initially but that they do become perfectly

organized (i.e., act identically to incumbents) eventually. Specifically,

all newly entered firms start as free riders but switch into non-free riders

(i.e., join the perfectly organized firms) according to a Poisson process

marked by the hazard rate φ. This switch is synchronized across all

entrants in the sense that at any given time, new entrants either will all

be free riders or will all be non-free riders. Furthermore, we assume that

37

the switch to non-free rider status is permanent, so that eventually all

firms are perfectly organized. Observe that φ provides a natural

parameter for the extent of the free-riding problem since newcomers are

expected to remain free riders for a period equal to 1/φ. Our basic model

implicitly assumes that φ is infinite.

We begin by studying the all-lobby outcome, that is, where both

high- and low-demand sectors lobby. Free riding complicates the

calculation of the expected value of entering because we must take

account of the probabilities that (i) the sector sees its demand change and

(ii) the entrant experiences a shift in its free-riding status. Incumbent

firms in this case will have one of four possible values: uHV , , uLV , , HV or

LV . These are, respectively, the value of an incumbent facing high or

low demand when entrants are unorganized (as shown by the subscript

u) and when the entrants have joined the lobby (as shown by a lack of

the subscript).

Three instantaneous probabilities are relevant to an incumbent’s

value. These are:

(i) the probability that the sector experiences a shift in demand,

λdt;

(ii) the probability that entrants become non-free riders, φdt;

(iii) the probability that the sector experiences both a change in

demand and entrants become non-free riders, λφ(dt)2.

38

Taking account of these at the limit d 0t → , VH and VL are still

determined by (14); the expected values of an incumbent in the various

states when entrants are unorganized are then

(18) , , , , ,

, , , , ,

( ) ( ),

( ) ( ),H u H u H u L u H u H

L u L u H u L u L u L

rV b V V V V

rV b V V V V

λ φλ φ

= − − − −= + − − −

where the values of b are the “flow rewards” to incumbents in the

various states (see Appendix A.2 for computational details).

The related value equations for entrants are:

(19) ( ) ( ),

( ) ( ),H H H L H H

L L H L L L

rJ J J J V

rJ J J J V

π λ φπ λ φ

= − − − −= + − − −

where JH and JL are the values of free-riding firms when the sector under

evaluation is facing high and low demand, respectively.

Since free riders do not contribute to lobbying expenses, the flow

benefit of being a free rider in both the high and low states of demand

exceeds the flow benefit of being an incumbent:

(20) , ,0, 0,H H u H L L u Lb bπ γ π γ− ≡ > − ≡ >

where γH and γL are constants.

The free-entry condition in this extension is JH = F.

Would high-demand incumbents lobby?

In the basic model, incumbents in the high-demand sector were

indifferent to lobbying when N=N*, since lobbying neither brought them

any benefits nor harmed their value. Now we turn to evaluating whether

high-demand sectors would still be indifferent to lobbying.

39

Section 3 established that the value of high-demand incumbents

in the only-losers-lobby outcome was equal to F. To see whether high-

demand sectors would be indifferent to lobbying, we check whether the

value of incumbents at the moment they lobby–that is, at the instant of

entry when entrants are still free riders, namely VH,u from (18)–is less

than F. Toward this end we solve (18) and (19) for the values of

incumbents in the four possible states of the world (high or low demand

and entrants free riding or not). The solutions, though intuitive, are not

especially transparent, but for our purpose we need only consider the

difference JH–VH,u, which can be written as (see Appendix A.2. for

details)

(21) ,

( ).

( )( 2 )H L

H H u

rJ V

r r

φ λ γ φγφ φ λ

+ + +− =+ + +

Given (20), we know that this expression is positive for any finite φ.

Moreover, this difference tends to zero as φ approaches infinity.

What this reasoning shows is that, starting from N = N*,

incumbents facing high demand in the OLL outcome would never agree

to lobby if there were any chance that free entrants would free ride, even

40

for an infinitely short time. This result reinforces our assertion that the

only-losers-lobby outcome is focal.18

4.2. Technology shocks instead of demand shocks

The basic model assumes stochastic preferences in order to generate

stochastic demand functions. In this section, we show that nothing would

change by instead assuming stochastic technology. Hence, we assume

that the sector-specific marginal costs are random variables βm that are

independently and identically distributed across sectors. Specifically,

(1 1/ ) , (1 1/ ) m G Bβ σ β σ β∈ − − for all m, where βG < βB; G is a

mnemonic for good and B stands for bad. Under Dixit–Stiglitz

monopolistic competition and within-sector symmetry, the price charged

by all sector-m firms is βm/(1-1/σ).

Moreover, we introduce some substitutability across sectors by

assuming that preferences are 1 1/ 1/(1 1/ )

1( ) , 1

M

mmU A D θ θ θ− −

== + >∑ . Given

the law of large numbers, total expenditure on sector m’s varieties is

18 The idea here is akin to the “trembling hand” refinement. If incumbents did make a

mistake and lobbied in the high state, thus raising the number of firms to the point

where JH = F, then they would continue to lobby because doing otherwise would lower

their value even further. This result, however, relies on the lack of exit. If firms did

exit, a one-time mistake would be corrected eventually. We thank Thierry Verdier for

this observation.

41

(22) 1

1 1

( ).

( / 2)( )m m

m mG G B B

Np cM

θ

θ θτ β

τ β τ β

−

− −=+

Now redefining αH and αL as equal to the right-hand side of expression

(22) evaluated at βm equal to (1-1/σ)βG and (1-1/σ)βB, respectively, we

note that the relation αH > αL still holds and hence all other derivations

in the paper carry through unaltered.

4.3. Sunset industries

As we stated in the Introduction, the literature on sunset

industries highlights that these industries continue to decline despite the

protection they receive, assuming they get protection in the first place. A

simple extension of our model captures this idea; note that our model

allows for endogenous lobbying decisions, so we do not assume that

these industries are protected a-priori.19

We first assume that firms are “dying” at a Poisson rate δ, so that

N can decrease as well as increase. Next, for simplicity we still assume

that the shocks occur on demand. But now we assume that once a

negative shock has hit industry m (αm = αL), demand will not recover. In

other words, shocks are permanent (and the cells of the first row of

Table 1 now contain the numbers 1 and 0, respectively; that is, the low

19 In this case also, two Markov perfect equilibria exist: the looser-only-lobby MPE and

the all-lobby MPE. Using an argument similar to that in Section 3.4, we can claim that

the former is focal: VH is equal to F in both MPEs, but VL is larger in the former than in

the latter.

42

state of the world is an absorbing state). Together, these modifications

imply that equation (14) must be replaced by

(23)

( ) , ( ) ( )

, ,

L L H H H L

L L H LL H

r V b r V b V V

b b b bV V

r r r

δ δ λ

δ δ δ λ

+ = + = − −⇔

−= = ++ + + +

where (as before) VH>VL holds without ambiguity whenever bH>bL.

The free-entry condition (15) implies VH = F, which once again

pins down the equilibrium number of firms. We call it N* so that Figure

1 illustrates the present extension as well. In particular, we concentrate

on the MPE in which only losers lobby. Note that dying firms are

immediately replaced by new entrants, so N = N* as long as α = αH.

Consider now what happens when, at some random time T,

demand falls permanently to αL. At time T, the number of firms N*

implies that the value of each firm in the affected sector falls to

OLLLV F< . In words, despite the fact that firms in this sector are now

lobbying, their value is smaller than the opportunity cost of capital and

so no new firms will enter the sector. What is new is that the mass of

firms is now decreasing at a rate δ, so that OLLLV increases over time

(remember that bL = BL/N and that BL is constant). This suggests that N

and OLLLV evolve over time as plotted in Figure 2 below.

Figure 2 plots time on the horizontal axis and, on the vertical

axis, plots both the number of firms and the value of a typical firm in a

representative sunset industry. Assume now that this sector is hit by the

shock at time T. First, as can be seen in the figure, OLLLV “overshoots” at

43

the time of the shock. Second, as the number of firms shrinks over time,

OLLLV returns to its steady-state value. At time T+∆T, OLL

LV F= is

expected to hold again and the number of firms no longer changes: N =

N0.20

Figure 2: Sunset industries

To capture more fully the idea that the industry is a “sunset

industry”, assume now that α keeps falling over time at random intervals

without ever reaching 0. Namely, the values of α now form an infinite

sequence 1 2 1 0H J Jα α α α α +≡ > > > > > >L L and the Markov square

20 More formally, for any ε ++∈ R and for any ξ ++∈ R , there exists a positive real

number T∆ such that 0 ( )OLLLF V t ε≤ − < and

00 ( )N t N ξ≤ − < for all t T T≥ + ∆ .

F

time

VLOLL

N*

T

€

N0

, N

N

T+∆T

44

matrix has now an infinitely countable number of rows and columns

with identical terms 1 dtλ− along the main diagonal, λdt in each cell to

the left of the main diagonal, and zeroes everywhere else. Then N0(α),

the steady-state mass of firms given α < αH, keeps falling. Note however

that N0(α) > 0 for all α > 0.

This “tomorrow never dies” feature of the model is not the most

attractive, but it is a direct consequence of the fact that Dixit–Stiglitz

monopolistic competition never produces negative operating profits.

With more reasonable assumptions, there would exist a threshold α, call

it α0, at which N0(α0)<0. In such a case, all firms would have leave the

sector eventually.

To sum up the results of this section, we observe that a sector hit

by a permanent shock gets protection at equilibrium; yet despite the

protection received, this sector shrinks (there is a net exit of firms) over

time and, under reasonable assumptions, this sector eventually

disappears. We remark that the “sunset sector” would have disappeared

earlier if it could not successfully lobby the government for protection.

This suggests that the possibility of lobbying entails hysteresis of the

production mix at the aggregate level. Since successful, growing sectors

do not lobby, this might–in a proper general equilibrium model–reduce

growth or steady-state per capita incomes. (See also Grossman and

Helpman 1996 on this point.)

45

5. Conclusion

Despite differences in political institutions and laws, declining industries

account for the bulk of protection granted in all industrialized nations.

The GATT also asymmetrically favors ailing industries. This asymmetry

is curious because selfish governments should be equally interested in

the lobbying dollars of expanding and declining industries. Our paper

provides a political equilibrium explanation based on sunk entry costs.

We assume that industries spend money on lobbying to obtain profit-

boosting protection and note a strong asymmetry between the

appropriability of protection in contracting and expanding industries. In

expanding industries, rents attract new entrants that erode the rents, but

this is not true in ailing industries. Sunk entry costs (product

development, training, advertising, etc.) allow protection to raise profits

without attracting entry–as long as profits rise to a value not higher than

a normal return on sunk capital. Clearly, asymmetric appropriability

implies asymmetric lobbying, and the result is that losers get most of the

protection because losers lobby harder.

Policy implications

The analysis in our paper can also be used to shed light on the social

desirability of packaging protectionist policies with anti-entry policies

(such as a government monopoly or production quotas). Such packaging

is likely to lead to greater levels of protection because it increases the

incentives of all industries to lobby for protection. Consider, for instance,

an industry that is able to organize a cartel that prevents new production

and entry. Since entry is impossible, all sectors–both expanding and

46

contracting–will find that lobbying generates appropriable rents. As

Result 1 showed, all sectors will lobby and the overall outcome will be a

greater reduction in social welfare than would occur without the entry

barriers.

Most OECD countries have laws prohibiting this kind of

collusion; however, in certain industries such as medicine, the special

interest group itself regulates the flow of new entrants via control over

standards. Labor unions could serve a similar role. In the basic model

described here, labor was paid the going wage and all rents accrued to

firm owners. However, it is easy to imagine a model where an industry-

specific labor union manages to capture some or all of the rents created

by protection. In such a model, the labor unions that are able to control

the wage of new workers would benefit from higher tariffs in expanding

industries. In fact, many countries do (or did) sanction "closed shop"

rules that have exactly this effect. Alternatively, the fixed setup cost can

also be interpreted as investments in human capital; under this

interpretation, the model would explain why workers with skills specific

to ailing industries would lobby.

One obvious policy recommendation derives directly from this

analysis. Protectionist packages that place controls on domestic entry or

production are likely to attract greater lobbying efforts and thereby lead

to greater deviations from the social optimum. Consequently, prohibiting

such packaging of policies would lower equilibrium protection rates.

47

Appendix

A.1. Deriving equation (5)

In this appendix, we derive the government’s reduced form objective

function (5) in the text. From the industry demand functions, assuming

symmetry of varieties within an industry and p = 1 (which itself follows

from markup pricing and choice of numéraire and units), we have

(A.1) 1/(1 1/ )

1/ 1 1/( ) d .m mm m j

m m m

D N jN

σσ σα α

τ τ

−− −

≡ =

∫

Hence, the second term in the utility function reduces to

(A.2) 1 1

ln ln( ).M M

mm m m

m m m

Dαα ατ= =

=∑ ∑

As usual with quasi-linear utility, spending on Ac is a residual

and so the total demand for A, aggregating over all consumers, is

(A.3) 1

1 1

;

1 ; (1 ).

Mc

m m mm

M Mm

m m m mm mm m

A Y T N p c

Y N T N pcN

τ

α τστ

=

= =

= − −

= + = −

∑

∑ ∑

Here we have used the balanced budget assumption to define the level of

lump sum taxation, T. Aggregate consumer income Y equals labor

income (i.e., unity) plus all operating profits–which, given (4), are equal

to the second right-hand term in the expression for Y. Combining these

elements and using p = 1 yields

48

(A.4) 1 1 1

1 11 1 ( 1) ,

M M Mc m m

m m mm m mm m m

A N N cN

α ασ τ σ τ= = =

= + − = + −∑ ∑ ∑

where we have used symmetry to obtain cm = α/(Nmτm) and thus the final

expression on the right-hand side. Then, combining these expressions for

Ac and Dm we obtain expression (5) in the text.

To boost intuition and facilitate graphical representation of the

model, it is useful to rewrite W as

(A.5) 1 1

1 ( ) .1

M M

m m m m mm m

aW N D pc

aα

= =

= + Π + − + ∑ ∑

That is to say, indirect utility of consumers (and thus the utilitarian

social welfare function) is proportional to 1 plus the sum of operating

profit plus the sum of consumer surplus.

A.2. Deriving equation (21)

In order to understand how we derive the expressions in (18), first note

that VH,u for any dt can be written as

(A.6) d

, , ,

2 2,

d d d

(d ) [1 d d (d ) ] .

r tH u H u L u H

L H u

V b t e V t V t

V t t t t V

λ φ

φλ λ φ φλ

−= + +

+ + − − −

Rearranging and dividing all terms by dt then gives

(A.7)

dd

, , , ,

, ,

1[( )

d( ) ( ) d ];

r tr t

H u H u L u H u

H H u L H u

eV b e V V

tV V V V t

λ

φ φλ

−−− = + −

+ − + −

now, taking the limit dt→0 yields the result in (18).

49

The system given by (18) and (19) can be rewritten so as to solve

for JH–VH,u and JL–VL,u –namely, for the differences between the payoff

of the free-riders and of the contributors in each state:

(A.8) ,

,

,H H u H

L L u L

J Vr

J Vr

γφ λ λγλ φ λ

−+ + − = −− + +

where we have made use of (20). Using Cramer’s rule, it is now easy to

derive (21). Note also that the term VH–VL does not appear in the system

(A.8); rather, it is determined by (14).

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